Problem: Given $ m \angle AOB = 6x + 11$, $ m \angle BOC = 9x - 97$, and $ m \angle AOC = 154$, find $m\angle AOB$. $O$ $A$ $C$ $B$
Solution: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {6x + 11} + {9x - 97} = {154}$ Combine like terms: $ 15x - 86 = 154$ Add $86$ to both sides: $ 15x = 240$ Divide both sides by $15$ to find $x$ $ x = 16$ Substitute $16$ for $x$ in the expression that was given for $m\angle AOB$ $ m\angle AOB = 6({16}) + 11$ Simplify: $ {m\angle AOB = 96 + 11}$ So ${m\angle AOB = 107}$.